In this paper, our goal is to establish the relationship between solutions of local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, also Minty local sharp vector variational type inequality and sharp efficient solutions of vector optimization problems, under generalized approximate $\eta$-convexity conditions for locally Lipschitzian functions

Based on the definition of double fuzzy relations, two types of new rough set models are constructed, which are multi-granulation double fuzzy rough sets called optimistic and pessimistic multi-granulation double fuzzy rough sets, and some of their properties were studied. In addition, we study the relationship between optimistic and pessimistic multi-granulation double fuzzy rough sets and double fuzzy rough sets.

Arabic was the language of philosophy, logic, Islamic sciences and rhetorical linguistic sciences. It was used in the writing of all sciences generally and became the language of world culture. Although the other languages of the Islamic world had a little share, but all peoples of Islamic countries; Arabs and non-Arabs, Muslims and non-Muslims attributed to that movement appreciated. Hence, Arab sciences flourished in their bright ages. Arabic language was a cultural container of the ancient Greek and Latin intellectual heritage. As the ancient Greek and Latin sciences and literatures were translated into Arabic in the bright ages of Islam. Arab language was a strong bond for them, as a common human heritage for the centuries to save it from being lost, as Muslims used it to develop their sciences and arts, as Muslims in the East used the Western sciences and literatures in the modern age, because they are not Eastern or Western, but the common efforts of all humanity. Arabic language opened for the dictionaries ​​and other tongues of cross-fertilization, civil friction and simulation. Arabic had become the language of sciences: mathematics, astronomy, engineering, logic, philosophy, mysticism, agriculture, industry and economics by the continuous efforts of scientists in their scientific research, invention, experimentation, knowledge collection and classification in various fields, where orientalists recognized the Arab leadership. That scientific and literary civilization moved to Europe through Italy, Andalusia, Crusades and the Ottoman Caliphate. Europeans learned Arabic language, literature and sciences in the centers of Toledo, Fez and cities of Maghreb.

This text deals with exploring random solutions for generalized nonlinear variational inequality problems. Using the Fan-KKM theorem and Aumann's measurable selection theorem, we are able to prove the existence and uniqueness of random solution sets under the conditions of monotonicity and convexity. Additionally, we use Minty's lemma to demonstrate the compactness and convexity of the random solution sets.

This study aims to determine the present and future scopes of the digital economy in Bangladesh to build a developed and prosperous country by 2041. Simultaneously, it analyses the components of the Digital Economy from numerous perspectives from contributing to Bangladeshi economy with an adaptation of the 4th Industrial Revolution and emerging technologies. In the methodology section, qualitative approach is conducted to determine the research objectives where secondary data is used. Around 100 papers are collected and 51 articles are used for conducting this study. The findings of the study are to present the current state of the digital economy which is developing trends that contribute to national GDP for the adaptation of the 4IR for the transformation of smart Bangladesh. From the conceptual implication, companies and individuals are aware of the digital economy, which would lessen digital divide and create a strong link between technology and the economy. Furthermore, establishing customer confidence and trust would be a big issue for Bangladesh's digital platform economy in the future days. From a practical standpoint, IT industries and commercial organizations would have to deal with emerging 4IR and its technologies. The job market would also be expanded in a variety of areas, which would ultimately benefit the national economy. According to the study's conclusions, the digital economy is predicted to expand its commercial and corporate opportunities. Future research might be extended based on qualitative approach towards a digital Bangladesh and create a better developing economy.

A well-known result of Posner’s second theorem states that if the commutator of each element in a prime ring and its image under a nonzero derivation is central, then the ring is commutative. In the present paper, we extend this bluestocking theorem to an arbitrary ring with involution involving prime ideals. Further, apart from proving several other interesting and exciting results, we establish *-version of Vukman’s theorem [48, Theorem 1]. Precisely, we describe the structure of quotient ring A/L, where A is an arbitrary ring and L is a prime ideal of A. Further, by taking advantage of the *-version of Vukman’s theorem, we show that if a 2-trosion free semiprime ring A with involution admits a nonzero *-centralizing derivation, then A contains a nonzero central ideal. This result is in a spirit of the classical result due to Bell and Martindale [19, Theorem 3]. As the applications, we extends and unify several classical theorems proved in [6],[25,[42], and [48] . Finally, we conclude our paper with a direction for further research.

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

During the COVID-19 pandemic, the education sector of Bangladesh suffered a lot. To adapt to this uncertain situation, the online teaching-learning method was introduced for the first time in the dental colleges to continue regular classes. This qualitative study explored the in-depth perception among students of this new, affordable, flexible online learning method and to find out the scope of improvement of the delivery method. Two focus group discussions (FGD) were conducted, each including 6-8 participants (N=16, the male: female ratio was 7:9) for gaining an in-depth understanding of the perception of online teaching among the dental students. With the help of the trigger questions, the facilitator and moderators conducted both the FGDs. By analysing the Focus group discussion, four distinct themes were identified. The main themes extracted from the data refer to the difficulties which students faced during participation in online classes (e.g., low attention span, unusual timing of classes, internet accessibility, power cut, boring content, etc.), advantages of online learning (e.g., saves time, able to continue studying during the lockdown, saves money, avoids commuting, being safe during a pandemic situation, one can participate in classes if sick, etc.), disadvantages of online classes (e.g., not feasible for clinical classes and lab works, lack of social interactions, lack of group study, long screen time, lack of after class peer discussion, lack of engagement, etc.), and also scopes of improvements (e.g., technological training for staff, recorded classes, technological orientation for students, more engaging contents, online support, more interactive lessons, short duration of the class, break after 30-45 minutes and also teachers training for online facilitation, etc.). In Bangladesh, the online teaching-learning method is not a regular practice. Most of the institutions were forced to adopt this method on very short notice because of the COVID-19 pandemic lockdown. Online education in a clinical subject like dentistry requires a special training program, online content preparation, and interactive lesson delivery setup which are big challenges for a re-source-constrained medical education setup. The focus group discussion unveiled some key issues which indicated that there are many scopes for improvement in online teaching methods. With the help of the medical education department and through faculty development the online learning sessions can be made attractive as well as beneficiary for the key stakeholders.

To define the optimistic multiple-granulation (OMG) supra interior operator and the OMG-supra closure operator associated with a set A in a multiple-granulation approximation space, we used the concepts of the OMG-lower set OL (A) and the OMG-upper set OU (A). These operators create an approximate topological space known as optimistic multiple-granulation supratopological spaces. OMG-supra-open and OMG-supra-closed approximation sets are also defined, followed by OMG-supra-continuous approximation and OMG-irresolute approximation.

Irrigation and fertilizer are two essential factors affecting rice root traits and yield. In this respect, a pot experiment was performed at the boro (dry season irrigated) season of 2021-22 in the Department of Agronomy of Bangladesh Agricultural University, Mymensingh, Bangladesh. The variety Binadhan-10 was planted at two irrigation conditions i.e. saturation (S) and continuous flooding (CF); two potassium (K) dose e.g. 65 kg ha-1 (K65) and 98 kg ha-1 (K98) and two nitrogen (N) dose i.e. 140 kg ha-1 (N140) and 210 kg ha-1 (N210). The experiment was laid in split plot design and replicated thrice. The findings confirmed the effectiveness of irrigation, K and N on root number (RN), root length (RL), root volume (RV), leaf area index (LAI), total dry matter (TDM), yield attributes and yield. Considering interaction among irrigation, K and N, S condition with K65 and N140 showed best performance. At 80 DAT, the highest RN (373.00), RL (1700.00 cm), RV (8.90 cm3 hill-1), LAI (4.94) and TDM (25.83 g plant-1) was obtained from this combination. Grain yield (GY) and root traits except root porosity, showed a significant positive association. Grain yield (GY) was highest (27.12 g pot-1) in S condition with K65 and N140.

This research investigated the antihypertensive effects of tamarind products and compared their potentials based on their animal model’s data verified by molecular docking, multitarget interactions in network pharmacology, and dynamic simulation assays. The GC-MS characterized tamarind products were administered to the cholesterol-induced hypertensive Wistar albino rat models. Two-week-intervened animals were dissected to collect serum and organs which were respectively subjected to the analyses of hypertension-linked markers and tissue architectures. Lead biometabolites of tamarinds interacted with eight target receptors in molecular docking and dynamic simulation studies and they were tested for multitarget interactions using network pharmacological analyses. Results showed that serum alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), C-reactive protein (CRP), Troponin I, and lipid profiles were maximally reinstated by the phenolic-enriched ripened sour over the sweet tamarind flesh extracts, but seed extracts had a smaller influence. Among the tamarind’s biometabolites, Gamma-sitosterol (ϒ-sitosterol) was found to be the best ligand in managing hypertension via the possible ligand-receptor interactions with the guanylate cyclase which displayed the best drug-likeliness through the highest binding energy -9.3 Kcal. Multitargeted interactions-based degree algorithm and phylogenetic tree of pathways showed 14 targeted genes, of which NR3C1, REN, PPARG, and CYP11B1 hub genes, were consistently modulated by the ϒ-sitosterol to reduce hypertension and related risk factors. The dynamic simulation study showed that the P-RMSD values of ϒ-sitosterol-guanylate cyclase were stable between 75.00 to 100.00 ns at the binding pocket. The findings demonstrate that ripened sour tamarind extract may be supplemented to be a more prospective antihypertensive target or nutraceuticals affirming through advanced preclinical and clinical studies.